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DOI: 10.4230/LIPIcs.IPEC.2018.4
URN: urn:nbn:de:0030-drops-102050
URL: https://drops.dagstuhl.de/opus/volltexte/2019/10205/
Bringmann, Karl ; Husfeldt, Thore ; Magnusson, Måns
Multivariate Analysis of Orthogonal Range Searching and Graph Distances
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Abstract
We show that the eccentricities, diameter, radius, and Wiener index of an undirected n-vertex graph with nonnegative edge lengths can be computed in time O(n * binom{k+ceil[log n]}{k} * 2^k k^2 log n), where k is the treewidth of the graph. For every epsilon>0, this bound is n^{1+epsilon}exp O(k), which matches a hardness result of Abboud, Vassilevska Williams, and Wang (SODA 2015) and closes an open problem in the multivariate analysis of polynomial-time computation. To this end, we show that the analysis of an algorithm of Cabello and Knauer (Comp. Geom., 2009) in the regime of non-constant treewidth can be improved by revisiting the analysis of orthogonal range searching, improving bounds of the form log^d n to binom{d+ceil[log n]}{d}, as originally observed by Monier (J. Alg. 1980). We also investigate the parameterization by vertex cover number.
BibTeX - Entry
@InProceedings{bringmann_et_al:LIPIcs:2019:10205,
author = {Karl Bringmann and Thore Husfeldt and M{\aa}ns Magnusson},
title = {{Multivariate Analysis of Orthogonal Range Searching and Graph Distances}},
booktitle = {13th International Symposium on Parameterized and Exact Computation (IPEC 2018)},
pages = {4:1--4:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-084-2},
ISSN = {1868-8969},
year = {2019},
volume = {115},
editor = {Christophe Paul and Michal Pilipczuk},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2019/10205},
URN = {urn:nbn:de:0030-drops-102050},
doi = {10.4230/LIPIcs.IPEC.2018.4},
annote = {Keywords: Diameter, radius, Wiener index, orthogonal range searching, treewidth, vertex cover number}
}
| Keywords: | Diameter, radius, Wiener index, orthogonal range searching, treewidth, vertex cover number | |
| Seminar: | 13th International Symposium on Parameterized and Exact Computation (IPEC 2018) | |
| Issue date: | 2019 | |
| Date of publication: | 05.02.2019 |
